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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.tradoffs"></a><a class="link" href="tradoffs.html" title="Trading Accuracy for Performance">Trading Accuracy for Performance</a>
</h2></div></div></div>
<p>
      There are a number of <a class="link" href="../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policies</a> that can be used
      to trade accuracy for performance:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Internal promotion: by default functions with <code class="computeroutput"><span class="keyword">float</span></code>
          arguments are evaluated at <code class="computeroutput"><span class="keyword">double</span></code>
          precision internally to ensure full precision in the result. Similarly
          <code class="computeroutput"><span class="keyword">double</span></code> precision functions
          are evaluated at <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
          precision internally by default. Changing these defaults can have a significant
          speed advantage at the expense of accuracy, note also that evaluating using
          <code class="computeroutput"><span class="keyword">float</span></code> internally may result
          in numerical instability for some of the more complex algorithms, we suggest
          you use this option with care.
        </li>
<li class="listitem">
          Target accuracy: just because you choose to evaluate at <code class="computeroutput"><span class="keyword">double</span></code>
          precision doesn't mean you necessarily want to target full 16-digit accuracy,
          if you wish you can change the default (full machine precision) to whatever
          is "good enough" for your particular use case.
        </li>
</ul></div>
<p>
      For example, suppose you want to evaluate <code class="computeroutput"><span class="keyword">double</span></code>
      precision functions at <code class="computeroutput"><span class="keyword">double</span></code>
      precision internally, you can change the global default by passing <code class="computeroutput"><span class="special">-</span><span class="identifier">DBOOST_MATH_PROMOTE_DOUBLE_POLICY</span><span class="special">=</span><span class="keyword">false</span></code> on the
      command line, or at the point of call via something like this:
    </p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">val</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">erf</span><span class="special">(</span><span class="identifier">my_argument</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">make_policy</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;()));</span>
</pre>
<p>
      However, an easier option might be:
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// Or any individual special function header</span>

<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>

<span class="keyword">namespace</span> <span class="identifier">precise</span><span class="special">{</span>
<span class="comment">//</span>
<span class="comment">// Define a Policy for accurate evaluation - this is the same as the default, unless</span>
<span class="comment">// someone has changed the global defaults.</span>
<span class="comment">//</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;</span> <span class="identifier">accurate_policy</span><span class="special">;</span>
<span class="comment">//</span>
<span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS to declare</span>
<span class="comment">// functions that use the above policy.  Note no trailing</span>
<span class="comment">// ";" required on the macro call:</span>
<span class="comment">//</span>
<span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">accurate_policy</span><span class="special">)</span>


<span class="special">}</span>

<span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
<span class="comment">//</span>
<span class="comment">// Define a Policy for fast evaluation:</span>
<span class="comment">//</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">[</span>
<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">fast_policy</span><span class="special">;</span>
<span class="comment">//</span>
<span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS:</span>
<span class="comment">//</span>
<span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">fast_policy</span><span class="special">)</span>

<span class="special">}</span>

<span class="special">}</span>
</pre>
<p>
      And now one can call:
    </p>
<pre class="programlisting"><span class="identifier">math</span><span class="special">::</span><span class="identifier">accurate</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
</pre>
<p>
      For the "accurate" version of tgamma, and:
    </p>
<pre class="programlisting"><span class="identifier">math</span><span class="special">::</span><span class="identifier">fast</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
</pre>
<p>
      For the faster version.
    </p>
<p>
      Had we wished to change the target precision (to 9 decimal places) as well
      as the evaluation type used, we might have done:
    </p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
<span class="comment">//</span>
<span class="comment">// Define a Policy for fast evaluation:</span>
<span class="comment">//</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">promote_double</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;,</span> <span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">9</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">fast_policy</span><span class="special">;</span>
<span class="comment">//</span>
<span class="comment">// Invoke BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS:</span>
<span class="comment">//</span>
<span class="identifier">BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS</span><span class="special">(</span><span class="identifier">fast_policy</span><span class="special">)</span>

<span class="special">}</span>
<span class="special">}</span>
</pre>
<p>
      One can do a similar thing with the distribution classes:
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// or any individual distribution header</span>

<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">fast</span><span class="special">{</span>
<span class="comment">//</span>
<span class="comment">// Define a policy for fastest possible evaluation:</span>
<span class="comment">//</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">policies</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">promote_float</span><span class="special">&lt;</span><span class="keyword">false</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">fast_float_policy</span><span class="special">;</span>
<span class="comment">//</span>
<span class="comment">// Invoke BOOST_MATH_DECLARE_DISTRIBUTIONS</span>
<span class="comment">//</span>
<span class="identifier">BOOST_MATH_DECLARE_DISTRIBUTIONS</span><span class="special">(</span><span class="keyword">float</span><span class="special">,</span> <span class="identifier">fast_float_policy</span><span class="special">)</span>

<span class="special">}}</span> <span class="comment">// namespaces</span>

<span class="comment">//</span>
<span class="comment">// And use:</span>
<span class="comment">//</span>
<span class="keyword">float</span> <span class="identifier">p_val</span> <span class="special">=</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">fast</span><span class="special">::</span><span class="identifier">normal</span><span class="special">(</span><span class="number">1.0f</span><span class="special">,</span> <span class="number">3.0f</span><span class="special">),</span> <span class="number">0.25f</span><span class="special">);</span>
</pre>
<p>
      Here's how these options change the relative performance of the distributions
      on Linux:
    </p>
<div class="table">
<a name="math_toolkit.tradoffs.table_Distribution_performance_comparison_for_different_performance_options_with_GNU_C_version_9_2_1_20191008_on_linux"></a><p class="title"><b>Table 23.2. Distribution performance comparison for different performance options
      with GNU C++ version 9.2.1 20191008 on linux</b></p>
<div class="table-contents"><table class="table" summary="Distribution performance comparison for different performance options
      with GNU C++ version 9.2.1 20191008 on linux">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              <p>
                Function
              </p>
            </th>
<th>
              <p>
                boost 1.73
              </p>
            </th>
<th>
              <p>
                Boost<br> promote_double&lt;false&gt;
              </p>
            </th>
<th>
              <p>
                Boost<br> promote_double&lt;false&gt;<br> digits10&lt;10&gt;
              </p>
            </th>
<th>
              <p>
                Boost<br> float<br> promote_float&lt;false&gt;
              </p>
            </th>
</tr></thead>
<tbody>
<tr>
<td>
              <p>
                ArcSine (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.75<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.65<br> (33ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.65<br> (33ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (20ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ArcSine (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (5ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.20<br> (6ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ArcSine (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Beta (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.41<br> (437ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (139ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (137ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (99ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Beta (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.29<br> (360ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.23<br> (103ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (104ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (84ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Beta (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.17<br> (2587ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.60<br> (991ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.44<br> (893ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (620ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Binomial (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.97<br> (837ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.54<br> (324ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (265ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (211ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Binomial (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.90<br> (322ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (121ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (121ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (111ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Binomial (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.88<br> (3917ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.53<br> (1548ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.26<br> (1273ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1009ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Cauchy (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (20ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (20ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Cauchy (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.33<br> (4ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Cauchy (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.88<br> (45ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (48ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.79<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (24ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ChiSquared (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.54<br> (1002ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.79<br> (506ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (397ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (283ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ChiSquared (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.84<br> (295ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (86ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (61ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ChiSquared (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.76<br> (1664ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.84<br> (815ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.37<br> (609ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (443ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Exponential (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (19ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.87<br> (28ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.60<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (15ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Exponential (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.58<br> (30ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.84<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">2.00<br> (38ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (19ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Exponential (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.13<br> (26ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.17<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (24ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ExtremeValue (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.78<br> (57ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.81<br> (58ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.81<br> (58ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (32ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ExtremeValue (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.96<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (85ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.83<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (46ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                ExtremeValue (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (53ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (53ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (37ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                F (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.46<br> (817ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.58<br> (289ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (227ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (183ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                F (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.37<br> (361ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.18<br> (126ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (120ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (107ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                F (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.70<br> (2615ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (1241ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.03<br> (995ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (969ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Gamma (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.90<br> (714ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.46<br> (267ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.47<br> (269ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (183ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Gamma (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.75<br> (437ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.49<br> (113ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.51<br> (115ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (76ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Gamma (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.35<br> (1827ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.80<br> (755ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.22<br> (511ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (420ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Geometric (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.16<br> (29ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Geometric (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.44<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.44<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.56<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (16ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Geometric (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (25ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.12<br> (28ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (26ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (31ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Hypergeometric (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (66745ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (61922ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (62901ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (66289ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Hypergeometric (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.16<br> (73824ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (63790ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.02<br> (65130ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.09<br> (69844ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Hypergeometric (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (131293ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (166268ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (163105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.14<br> (149745ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseChiSquared (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.06<br> (1538ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.60<br> (803ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (657ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (502ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseChiSquared (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.42<br> (367ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.63<br> (135ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (126ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (83ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseChiSquared (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.92<br> (2328ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.66<br> (1322ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (963ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (797ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGamma (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.17<br> (806ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (359ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.18<br> (299ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (254ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGamma (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.26<br> (515ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.54<br> (151ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.49<br> (146ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (98ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGamma (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.02<br> (2187ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.69<br> (921ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.19<br> (645ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (544ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGaussian (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.89<br> (236ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.94<br> (242ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.99<br> (249ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (125ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGaussian (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.53<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.53<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.53<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (15ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                InverseGaussian (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.09<br> (3530ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.26<br> (3823ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.14<br> (3611ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1688ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Laplace (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.58<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.62<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.62<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (26ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Laplace (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.56<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Laplace (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.39<br> (39ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (40ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (38ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (28ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                LogNormal (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.12<br> (225ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.33<br> (141ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (144ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (106ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                LogNormal (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.68<br> (74ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (76ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.70<br> (75ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (44ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                LogNormal (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.75<br> (105ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.68<br> (101ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (84ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (60ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Logistic (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (41ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.74<br> (47ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Logistic (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (43ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (27ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Logistic (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.23<br> (37ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.23<br> (37ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (38ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (30ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NegativeBinomial (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.51<br> (1354ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.80<br> (540ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.37<br> (410ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (300ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NegativeBinomial (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.62<br> (445ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (131ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.07<br> (132ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (123ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NegativeBinomial (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.26<br> (7468ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.27<br> (2918ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (2294ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.15<br> (2649ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralBeta (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.88<br> (2083ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.80<br> (769ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.61<br> (689ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (427ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralBeta (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.83<br> (1265ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (511ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.42<br> (468ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (330ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralBeta (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">7.51<br> (55809ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.59<br> (19273ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.26<br> (16812ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (7433ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralChiSquared (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.90<br> (4498ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.82<br> (2821ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (2220ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1552ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralChiSquared (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.52<br> (953ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.61<br> (436ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.54<br> (416ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (271ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralChiSquared (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.15<br> (31465ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.33<br> (17712ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.56<br> (11870ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (7586ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralF (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.26<br> (1828ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (667ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.36<br> (584ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (429ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralF (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.98<br> (1506ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.49<br> (564ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (488ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (378ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralF (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.52<br> (29414ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.57<br> (10228ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (8543ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (6504ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralT (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.79<br> (6416ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.72<br> (2907ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (2572ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1691ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralT (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.41<br> (4034ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.93<br> (2284ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.75<br> (2065ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (1182ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                NonCentralT (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.06<br> (68590ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.17<br> (29386ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.65<br> (22334ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (13546ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Normal (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.24<br> (150ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.34<br> (90ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.28<br> (86ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (67ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Normal (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.55<br> (34ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.50<br> (33ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.59<br> (35ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (22ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Normal (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.68<br> (57ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.18<br> (40ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.24<br> (42ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (34ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Pareto (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (49ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.46<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.40<br> (49ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (35ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Pareto (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.95<br> (86ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.95<br> (86ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.09<br> (92ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (44ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Pareto (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.76<br> (51ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.79<br> (52ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.72<br> (50ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (29ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Poisson (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.38<br> (264ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.56<br> (122ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.45<br> (113ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (78ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Poisson (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">4.19<br> (218ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.54<br> (80ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (79ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (52ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Poisson (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">3.04<br> (1193ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.38<br> (540ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.35<br> (528ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (392ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Rayleigh (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.35<br> (23ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.41<br> (24ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (17ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Rayleigh (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.68<br> (37ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.64<br> (36ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.64<br> (36ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (22ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Rayleigh (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.04<br> (27ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (26ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.08<br> (28ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                SkewNormal (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.43<br> (691ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (633ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (635ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (483ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                SkewNormal (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.07<br> (174ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (110ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.29<br> (108ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (84ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                SkewNormal (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">2.16<br> (6788ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.85<br> (5813ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.31<br> (4118ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (3143ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                StudentsT (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">6.44<br> (1893ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.23<br> (656ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="red">2.21<br> (650ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (294ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                StudentsT (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="red">6.58<br> (724ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.60<br> (176ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.52<br> (167ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (110ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                StudentsT (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="red">5.79<br> (2959ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.87<br> (954ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.86<br> (951ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (511ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Weibull (CDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.73<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.75<br> (70ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (40ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Weibull (PDF)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.98<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.98<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.98<br> (117ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (59ns)</span>
              </p>
            </td>
</tr>
<tr>
<td>
              <p>
                Weibull (quantile)
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="blue">1.21<br> (69ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.19<br> (68ns)</span>
              </p>
            </td>
<td>
              <p>
                <span class="green">1.00<br> (57ns)</span>
              </p>
            </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div>
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